Abstract
The ADE two-dimensional interaction-round-a-face statistical models are formulated on a fluctuating planar lattice. The continuum limit of such systems is described by the minimal conformal theories coupled to quantum gravity. All these models can be reformulated in terms of a gas of self-avoiding noninteresecting loops on a random planar graph. This representation allows us to calculate the partition function and the susceptibilities of the order parameters in the case of lattices with spherical topology. The scaling dimensions of the order parameters are shown to form a linear spectrum.
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